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Working backwards in such type of questions saves me more time than actually solving them. So starting with the middle unit which is 6
Six does not fit the ratio
But eight does so the answer is 8 D.
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A 12-liter mixture of apple juice and carrot juice contains apple juice and carrot juice in a 1:3 ratio by volume. What amount of the mixture, by volume, should be replaced with an equal amount of apple juice to change the ratio of apple juice to carrot juice to 3:1 by volume ?

A. 3
B. 4
C. 6
D. 8
E. 10


 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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Original ratio:
Apple:Carrot = 1:3

Let the apple juice to be mixed be "x"

So, x+1/3 = 3/1
x = 8

The correct answer is D
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A 12-liter mixture of apple juice and carrot juice contains apple juice and carrot juice in a 1:3 ratio by volume. What amount of the mixture, by volume, should be replaced with an equal amount of apple juice to change the ratio of apple juice to carrot juice to 3:1 by volume ?

A. 3
B. 4
C. 6
D. 8
E. 10


 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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JuiceRatioVolume in liters
Apple13
Carrot39
Total12

Say x liters of the mixture is replaced with x liters of apple juice.

As the mixture is in the ratio of 1:3 of Apple to Carrot Juice, x/4 liter of Apple juice is replaced with x liters of Apple juice and 3x/4 liter of Carrot juice is removed.

Therefore,
New Volume of Apple Juice = 3 - x/4 + x = 3 + 3x/4
New Volume of Carrot Juice = 9 - 3x/4
->
JuiceNew RatioVolume in liters
Apple33 + 3x/4
Carrot19 - 3x/4
Total12

[3+3x/4]/[9-3x/4] = 3/1

3+3x/4= 27-9x/4

12x/4=24

x= 8 liters


Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A 12-liter mixture of apple juice and carrot juice contains apple juice and carrot juice in a 1:3 ratio by volume. What amount of the mixture, by volume, should be replaced with an equal amount of apple juice to change the ratio of apple juice to carrot juice to 3:1 by volume ?

A. 3
B. 4
C. 6
D. 8
E. 10


 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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Total mixture = 12 litres
Apple Juice = 12/4 = 3 litres
Carrot Juice = 12 x 0.75 = 9 litres

Now when x litres of juice removed, its also removed in same mixture ratio
So,
Apple juice removed= 0.25x
Carrot juice removed= 0.75x

Now replacing with x litres of pure apple juice

New mixture amount would result in
Apple juice = 3 - 0.25x + x =3 + 0.75x
Carrot juice = 9 - 0.75x

So, new ratio
=> ((3 + 0.75x) / (9 - 0.75x)) = 3/1
=> x = 8

D. 8 litres of the mixture should be replaced with pure apple juice
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Let x be the mixture replaced

1/3 = 3/4(1 - x/12)

1/3 - 1 = - x/12

-2/3 = - x/12

x = 12 x 2/3

x = 8
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